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State whether 51 is prime or composite. Exercise composite
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State whether 97 is prime or composite. prime Exercise
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Write the prime factorization of 90. 2 3 2 5 Exercise
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Write the prime factorization of 150. 2 3 5 2 Exercise
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Find the greatest common factor of 90 and 150. 2 3 5 = 30 Exercise
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multiples of 3 1 x multiples of 4 5 x multiples of 3 multiples of 4 2 x 6 x 3 x 7 x 4 x 8 x 369 12 48 16 15 20 18 24 21 28 24 32
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Least Common Multiple The least common multiple of two or more numbers is the smallest number that is a multiple of each of the given numbers.
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List multiples to find the LCM of 10 and 12. The LCM of 10 and 12 is 60. 10: 10, 20, 30, 40, 50, 60, 70… 12: 12, 24, 36, 48, 60, 72, 84… Example 1
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Using Listing to Find the Least Common Multiple 1.List the multiples of each number. 2.Identify the first common multiple in each list of multiples.
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List multiples to find the LCM of 8 and 6. 24 Example
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List multiples to find the LCM of 15 and 36. 180 Example
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Using Exponential Form to Find the LCM 1.Write the prime factorization of each number in exponential form.
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Using Exponential Form to Find the LCM 2. Identify all the prime factors, both the common and different prime factors, that appear in the factorizations.
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Using Exponential Form to Find the LCM 3. Find the product of all the prime factors, using only the highest power of each that appears in any of the factorizations.
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Find the LCM of 30 and 45. = 90 30: 2 3 5 45: 3 3 5 = 3 2 5 LCM = 2 3 2 5 Example 2
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Find the LCM of 12, 28, and 75. = 2,100 12: 2 2 3 = 2 2 3 28: 2 2 7 = 2 2 7 LCM = 2 2 3 5 2 7 75: 3 5 5 = 3 5 2 = 4 3 25 7 Example 3
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Use prime factorizations to find the LCM of 40 and 50. 200 Example
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Use prime factorizations to find the LCM of 21 and 49. 147 Example
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Use prime factorizations to find the LCM of 32, 18, and 72. 288 Example
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Use prime factorizations to find the LCM of 42, 45, and 63. 630 Example
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LCM of 4x and 4x 2
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3ab 2 5a2b5a2b 5a2b5a2b
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3y3y 3y3y 4z4z 4z4z
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Find the LCM of 15x 3 y and 21x 2. LCM = 105x 3 y 15x 3 y: 3 5 x x x y 21x 2 : 3 7 x x 3 5 7 = 105 x 3 and y Example 4
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Find the LCM of 12ab and 15b 2 c. 60ab 2 c Example
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Find the LCM of 63x 2 y 3 and 72x 3 y 4. 504x 3 y 4 Example
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Find the LCM of 8mn 2, 36m 3 n and 9m. 72m 3 n 2 Example
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Find the LCM of 84r, 21s and 14t. 84rst Example
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Find the GCF and LCM of 36 and 48. GCF: 12; LCM: 144 Exercise
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Find the GCF and LCM of 12, 18, and 24. GCF: 6; LCM: 72 Exercise
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For any two numbers, what would be the least common factor? 1 1 Exercise
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For any two numbers, what would be the greatest common multiple? Exercise
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When you reduce fractions such as, are you using an LCM or a GCF? How? 350 400 Exercise
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When you add fractions such as and to get, are you using an LCM or a GCF? How? 1616 1616 1818 1818 7 24 Exercise
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